Bias Correction for Covariance Parameter MLEs in GLMMs

• Activity Number: 239
• Type: Contributed
• Date/Time: Monday, August 5, 2013 : 2:00 PM to 3:50 PM
• Sponsor: Biometrics Section
• Author(s): Elizabeth Claassen*+ and Christopher Gotwalt and Walt W. Stroup
• Companies: University of Nebraska-Lincoln and SAS Institute and University of Nebraska-Lincoln
• Keywords: Maximum Likelihood Estimation ; Generalized Linear Mixed Models ; Firth correction ; REML

Abstract

Maximum likelihood estimation in linear mixed models (LMMs) is known to produce biased estimates of covariance parameters. Restricted Maximum Likelihood (REML) is the standard method for estimation in LMMs because of its bias reduction properties. While less commonly appreciated, MLEs of covariance parameters in generalized linear mixed models (GLMMs) are similarly biased. Firth (1993) developed a bias adjustment for MLEs. Gotwalt (2012) showed REML to be a special case of the Firth adjustment for LMMs with linear covariance structures. We will show preliminary work towards developing a Firth correction for GLMMs. For certain GLMMs this could be viewed as a generalized analog to REML.